 reserve x,y,X,Y for set;
reserve G for non empty multMagma,
  D for set,
  a,b,c,r,l for Element of G;
reserve M for non empty multLoopStr;
reserve H for non empty SubStr of G,
  N for non empty MonoidalSubStr of G;

theorem
  the carrier of MFuncs X = Funcs(X,X) &
  the multF of MFuncs X = (X-composition)||Funcs(X,X) &
  1.MFuncs X = id X
proof
  the_unity_wrt op(GFuncs X) = id X & the multMagma of MFuncs X = GFuncs X
  by Def22,Th75;
  hence thesis by Def40,Th17,Th74;
end;
